As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Fifty children, ranging in age from 4 to 10, were individually administered a series of tasks involving different combinations of 2 items selected from a discrete set of items. Analyses of their performances revealed a series of six, increasingly sophisticated, solution strategies ranging from random number selection of items to a systematic…